Electron device which controls quantum chaos and quantum chaos controlling method

ABSTRACT

An electron device which controls quantum chaos wherein a quantum chaos property is controlled extensively and externally is provided. The electron device which controls quantum chaos is manufactured by using a single material. A heterojunction provided with a first region having an electron system characterized by quantum chaos and a second region having an electron system characterized by integrability is formed. The first region and the second region are adjacent to each other, and the heterojunction is capable of exchanging electrons between the first region and the second region. A quantum chaos property of an electron system in a system formed of the first region and the second region is controlled by applying to the heterojunction an electric field having a component perpendicular to at least a junction surface.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an electron device which controlsquantum chaos and a method of controlling quantum chaos, and,particularly, the invention is based on a novel principle.

2. Description of the Related Art

Intrinsic nonlinearity is important as a physical system in the field ofinformation processing. Electronic elements made from materials having acertain nonlinear response have heretofore been used. An example of theelectronic elements having nonlinear current/voltage characteristics isa two-terminal element having a differential negative resistance. Ofcourse, MOS-FETs support the modern technology as a three-terminalelement. These nonlinear electronic elements are bonded in a linearelectronic circuit to construct a nonlinear information processor forexecuting an arbitrary calculation.

However, problems caused by the high integration have been detected withsuch electronic circuit. For example, a heating problem has been raised.The heating caused by an intrinsic electric resistance is mandatory forgenerating the nonlinearity of the electronic element as well as isnecessary and essential for executing information processing.

In order to avoid the problem, attempts of reducing the number ofelements by increasing the nonlinearity of each of the componentelements have been made. In the course of the attempts, a componentelement having a so strong nonlinearity that exhibits chaos hasinevitably been desired. In the case of quantizing a classical systemexhibiting chaos, a behavior of the quantum system is characterized byquantum chaos.

In turn, in the fine component element, electrons trapped in the elementbehave as quantum-mechanic particles. From this standpoint, therefore,the component element showing the quantum chaos is attracting attention.

The inventor of this invention has theoretically clarified that a changein a structure of a material contributes to a control on quantum chaosin an electronic system of the structure. Examples of possible controlare a control achieved by adjusting an effective size of interactionbetween electrons through a change in size of a quantum dot (Non-PatentLiterature 1), a control achieved by controlling a fractal dimension ina fractal aggregate (Non-Patent Literatures 2, 3, and 4), a structurecontrol in a multiplexed hierarchical structure (Non-Patent Literature5), and the like.

Non-Patent Literature 1: R. Ugajin, Physica A 237, 220 (1997)

Non-Patent Literature 2: R. Ugajin, S. Hirata, and Y. Kuroki, Physica A278, 312 (2000)

Non-Patent Literature 3: R. Ugajin, Phys. Lett. A 277, 267 (2000)

Non-Patent Literature 4: R. Ugajin, Physica A 301, 1 (2001)

Non-Patent Literature 5: R. Ugajin, J. Nanotechnol. 1, 227 (2001)

Further, the inventor has theoretically revealed that it is possible tocontrol the Mott metal-insulator transition by the use of the electricfield effect in an array formed by aggregating a certain type of quantumdots (Non-Patent Literatures 6, 7, 8, and 9). In turn, it has beenreported that it is possible to control a conductivity of a junctionsystem consisting of a layer of a high impurity scattering and a layerof a high purity with a remarkably low impurity scattering by applyingan electric field to the system (Non-Patent Literatures 10 and 11).

Non-Patent Literature 6: R. Ugajin, J. Appl. Phys. 76, 2833 (1994)

Non-Patent Literature 7: R. Ugajin, Physica E 1, 226 (1997)

Non-Patent-Literature 8: R. Ugajin, Phys. Rev. B 53, 10141 (1996)

Non-Patent Literature 9: R. Ugajin, J. Phys. Soc. Jpn. 65, 3952 (1996)

Non-Patent Literature 10: H. Sakaki, Jpn. J. Appl. Phys. 21, L381 (1982)

Non-Patent Literature 11: K. Hirakawa, H. Sakaki, and J. Yoshino, Phys.Rev. Lett. 54, 1279 (1985)

Also, it has been reported that generation of quantum chaos is detectedby using quantum level statistics (Non-Patent Literatures 12 and 13).

Non-Patent Literature 12: L. E. Reichl, The transition to chaos: inconservative classical systems: quantum manifestations (Springer, NewYork, 1992)

Non-Patent Literature 13: F. Haake, Quantum Signatures of chaos,(Springer-Verlag, 1991)

Also, the Berry-Robnik parameter ρ is known as a parameter forquantitatively detecting a modulation in quantum chaos property(Non-Patent Literature 14), and it is known that p is a volume ratio ofa regular region in a phase space in the scope of semi-classicalapproximation (Non-Patent Literature 15).

Non-Patent Literature 14: M. V. Berry and M. Robnik, J. Phys. A (Math.Gen.) 17, 2413 (1984)

Non-Patent Literature 15: B. Eckhardt, Phys. Rep. 163, 205 (1988)

In addition, the neutron transmutation doping (NTD) which is a method ofdoping a semiconductor through a nuclear reaction of neutrons of stableisotopes has been developed (Non-Patent Literature 16).

Non-Patent Literature 16: K. M. Itoh, E. E. Haller, W. L. Hansen, J. W.Beeman, J. W. Farmer, A. Rudnev, A. Tkhomirov, and V. I. Ozhogin, Appl.Phys. Lett. 64, 2121 (1994)

SUMMARY OF THE INVENTION

With the above-mentioned conventional quantum chaos generation methods,the range of the control on the quantum chaos property is limited.Therefore, a technology of more extensively controlling the quantumchaos property has been demanded. Further, in order to control thequantum chaos property more conveniently, it is desirable that thequantum chaos property be externally controlled.

Accordingly, an object of the present invention is to provide anelectron device which controls quantum chaos wherein the quantum chaosproperty is extensively and externally controlled and a quantum chaoscontrolling method.

Another object of the invention is to provide an electron device whichcontrols quantum chaos wherein the quantum chaos property is extensivelyand externally controlled when a single material is used and a quantumchaos controlling method.

The inventor has conducted intensive researches to solve the aboveproblems of the conventional technologies and has found that, in ajunction structure where a region which is in a metallic state andexhibits quantum chaos is bonded with a region which is in an Andersonlocalization state and has integrability, it is possible to moreextensively control quantum chaos property of an electron system trappedin the structure by an electric field effect as compared with theconventional technologies and that it is possible to perform theextensive control externally and with the use of a single material.

It is known that GUE (Gaussian unitary ensemble) quantum chaos having astronger nonlinearity is generated thanks to a random magnetic filedwhich is realized by an addition of a magnetic impurity such asmanganese (Mn). The inventor has found that, in a junction structurewhere a region which is in a metallic state and exhibits GUE quantumchaos having a strong nonlinearity is bonded with a region which is inan Anderson localization state and has integrability, it is possible toextensively control a quantum chaos property of an electron systemtrapped in the structure by an electric field effect and that it ispossible to perform the extensive control externally and with the use ofa single material.

This invention has been accomplished as a result of studies conductedbased on the above findings. More specifically, to solve the aboveproblems, according to a first aspect of the invention, there isprovided an electron device which controls quantum chaos comprising aheterojunction which is provided with a first region having an electronsystem characterized by quantum chaos and a second region having anelectron system characterized by integrability, the first region and thesecond region being adjacent to each other, and the heterojunction beingcapable of exchanging electrons between the first region and the secondregion, wherein a quantum chaos property of an electron system in asystem formed of the first region and the second region is controlled byapplying to the heterojunction an electric field having a componentperpendicular to at least a junction surface.

According to a second aspect of the invention, there is provided aquantum chaos control method comprising using a heterojunction which isprovided with a first region having an electron system characterized byquantum chaos and a second region having an electron systemcharacterized by integrability, the first region and the second regionbeing adjacent to each other, and the heterojunction being capable ofexchanging electrons between the first region and the second region, andcontrolling a quantum chaos property of an electron system in a systemformed of the first region and the second region by applying to theheterojunction an electric field having a component perpendicular to atleast a junction surface.

As used herein, “heterojunction” means a junction wherein the firstregion having the electron system characterized by quantum chaos and thesecond region having the electron system characterized by integrabilityare adjacent to (or contact with) each other, i.e., the heterojunctionis the junction formed when two regions which are different incharacteristic of electron system are adjacent to each other. Theheterojunction may be formed either by using a single material or byusing different materials. The electron system in the heterojunction isrefereed to as heterotic phase. A double heterojunction may be formed byproviding the first regions on each sides of the second region, i.e., bysandwiching the second region by the first regions. Likewise, the doubleheterojunction may be formed by providing the second regions on eachsides of the first region, i.e., by sandwiching the first region by thesecond regions. The electron system in the double heterojunction isreferred to as double heterotic phase.

The types of the materials to be used for the heterojunction areparticularly not limited. Specific examples of the materials may besemiconductors (elementary semiconductors such as Si and Ge; III-Vcompound semiconductors such as GaAs, GaP, and GaN; II-VI compoundsemiconductor such as ZnSe). Each of the first region and the secondregion may typically be crystalline and generally has the shape of alayer. More specifically, the heterojunction is formed by growing acrystal layer which serves as the first region and a crystal layer whichserves as the second region through various crystal growth methods. Atransition region may sometimes be present in a boundary region betweenthe first region and the second region, but there is no fundamentaldifference in terms of expression of necessary physicality when thetransition region is present.

The first region having the electron system characterized by quantumchaos is typically in a metallic state, and the second region having theelectron system characterized by integrability typically has a randommedium or a random magnetic field is present in the second region. Therandom medium is not particularly limited so far as a random potentialworks with electrons, and typical examples thereof may be impurity and alattice defect. The random magnetic field is typically generated by anaddition of magnetic impurity such as Mn.

In the above-described heterojunction, a maximum length in a directionalong the junction surface may favorably be less than a coherence lengthof electrons from the standpoint of quantum chaos expression.

An electrode for electric field application is ordinarily provided forthe purpose of applying to the heterojunction an electric field having acomponent perpendicular at least to the junction surface. For example,the electrode is provided in at least one of the first region and thesecond region included in the heterojunction. In this case, aninsulating film is provided for the purpose of electrical insulation ofthe electrode. Particularly, in the case where each of the first regionand the second region has the layer shape, the insulating film is formedon at least one of the first region and the second region to provide theelectrode.

In the electron device which controls quantum chaos, a wiring forinputting/outputting an electric signal is provided in addition to theheterojunction and the electrode when so required.

The above-described electric field application, i.e. the control on thequantum chaos by the electric field effect, accompanies the Andersontransition which is a metal/insulator transition; however, by setting atransfer between the first region and the second region to be equal orless than a transfer in the first region or a transfer in the secondregion, preferably to be sufficiently less (to be ⅔ or less, forexample) than the transfers in the first region and the second region,it is possible to rapidly cause the Anderson transition using theelectric field effect. In order to set the above transfers, a tunnelbarrier region is provided between the first region and the secondregion. Typical examples of the above structure may be such that each ofthe first region and the second region is formed from GaAs and thetunnel barrier region is formed from AlGaAs. Also, in order to manifestan effect of this invention favorably at a high temperature, it iseffective to employ a structure formed by using materials having alarger band offset, wherein each of the first region and the secondregion is formed from InGaAs and the tunnel barrier region is formedfrom AlGaAs.

In this invention, it is possible to control critical field intensitywith which a transition from quantum chaos to an integrable systemoccurs by controlling a Fermi level of the electron system. Therefore,by setting the Fermi level of the electron system to a predeterminedvalue in addition to the above electric field application, it ispossible to extensively control the quantum chaos property of theelectron system. It is possible to control the Fermi level of theelectron system by controlling a density of the electron system.

According to the invention with the above-described constitution, byapplying an electric field to the heterojunction formed of the firstregion having the electron system characterized by quantum chaos and thesecond region having the electron system characterized by integrability,it is possible to universally control the electron system of the systemincluding the first region and the second region from the state showinga typical quantum chaos to the state showing the Anderson localization.Further, this control is achieved irrelevant from the types of materialsused for forming the heterojunction. Also, by performing the control onthe Fermi level in combination with the electric field application, itis possible to extensively control the quantum chaos property. Further,it is possible to cause the Anderson transition rapidly by keeping thetransfer between the first region and the second region to be equal toor less than the transfers in the first region and the second region.

According to the invention, the heterojunction is formed by providingthereto the first region having the electron system characterized byquantum chaos and the second region having the electron systemcharacterized by integrability in such a fashion that the first regionand the second region are adjacent to each other and electrons areexchanged between the first region and the second region, and theelectric field having the component perpendicular at least to thejunction surface is applied to the heterojunction, thereby enabling toextensively and externally control the quantum chaos property of anelectron system of a system formed of the first region and the secondregion. Further, the extensive control is achieved with the use of asingle material. Also, by properly setting the transfers, it is possibleto rapidly cause the Anderson transition. Also, by controlling the Fermilevel of the electron system in addition to the electric fieldapplication, it is possible to more extensively control the quantumchaos property of the electronic system. Also, by using the doubleheterotic phase, it is possible to more extensively control the quantumchaos property.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating an electron state in atwo-dimensional random potential.

FIG. 2 is a schematic diagram showing results obtained by a simulationusing the model shown in FIG. 1.

FIG. 3 is a schematic diagram showing results obtained by a simulationusing the model shown in FIG. 1.

FIG. 4 is a schematic diagram showing a main part of an electron devicewhich controls quantum chaos according to a first embodiment of theinvention.

FIG. 5 is a schematic diagram showing results obtained by a simulationaccording to the first embodiment of the invention.

FIG. 6 is a schematic diagram showing results obtained by a simulationaccording to the first embodiment of the invention.

FIG. 7 is a sectional view showing a specific example of the electrondevice which controls quantum chaos according to the first embodiment ofthe invention.

FIG. 8 is a sectional view showing a manufacturing method of theelectron device which controls quantum chaos according to the firstembodiment of the invention.

FIG. 9 is a sectional view showing another example of the electrondevice which controls quantum chaos according to the first embodiment ofthe invention.

FIG. 10 is a schematic diagram showing results obtained by a simulationusing the model shown in FIG. 1.

FIG. 11 is a schematic diagram showing results obtained by a simulationusing the model shown in FIG. 1.

FIG. 12 is a schematic diagram showing results obtained by a simulationaccording to a second embodiment of the invention.

FIG. 13 is a schematic diagram showing results obtained by a simulationaccording to the second embodiment of the invention.

FIG. 14 is a schematic diagram showing results obtained by a simulationaccording to a third embodiment of the invention.

FIG. 15 is a schematic diagram showing results obtained by a simulationaccording to the third embodiment of the invention.

FIG. 16 is a schematic diagram showing results obtained by a simulationaccording to the third embodiment of the invention.

FIG. 17 is a schematic diagram showing results obtained by a simulationaccording to the third embodiment of the invention.

FIG. 18 is a schematic diagram showing results obtained by a simulationaccording to a fourth embodiment of the invention.

FIG. 19 is a schematic diagram showing results obtained by a simulationaccording to the fourth embodiment of the invention.

FIG. 20 is a schematic diagram showing results obtained by a simulationaccording to the fourth embodiment of the invention.

FIG. 21 is a schematic diagram showing results obtained by a simulationaccording to the fourth embodiment of the invention.

FIG. 22 is a schematic diagram showing results obtained by a simulationaccording to the fourth embodiment of the invention.

FIG. 23 is a schematic diagram showing results obtained by a simulationaccording to the fourth embodiment of the invention.

FIG. 24 is a perspective view showing a specific example of a structureof an electron device which controls quantum chaos according to thefourth embodiment of the invention.

FIG. 25 is a diagram showing an energy band of the electron device whichcontrols quantum chaos according to the fourth embodiment of theinvention.

FIG. 26 is a schematic diagram showing a main part of an electron devicewhich controls quantum chaos according to a fifth embodiment of theinvention.

FIG. 27 is a schematic diagram showing results obtained by a simulationaccording to the fifth embodiment of the invention.

FIG. 28 is a schematic diagram showing results obtained by a simulationaccording to the fifth embodiment of the invention.

FIG. 29 is a schematic diagram showing results obtained by a simulationaccording to the fifth embodiment of the invention.

FIG. 30 is a schematic diagram showing results obtained by a simulationaccording to the fifth embodiment of the invention.

FIG. 31 is a sectional view showing a specific example of a structure ofan electron device which controls quantum chaos according to the fifthembodiment of the invention.

FIG. 32 is a diagram showing an energy band of the electron device whichcontrols quantum chaos according to the fifth embodiment of theinvention.

FIG. 33 is a sectional view showing a specific example of a structure ofan electron device which controls quantum chaos having a three layerstructure of localized layer/conductive layer/localized layer.

FIG. 34 is a diagram showing an energy band of the electron device whichcontrols quantum chaos shown in FIG. 33.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the invention will hereinafter be described.

First Embodiment

In the first embodiment, an electron device which controls quantum chaosusing a heterojunction which is a junction system of a region having anelectron system characterized by quantum chaos and a region having anelectron system characterized by integrability will be described.

Before describing the first embodiment, electrons on a two-dimensionalsquare lattice, more specifically an electron state in a two-dimensionalrandom potential, will be described.

Referring to FIG. 1, each side of the square lattice is L site, and dotsindicate lattice points. An operator for generating quantum ĉ_(p) ^(t)is defined on a p-th lattice point of the square lattice. Here,Hamiltonian Ĥ₂ of a quantum system is defined as follows:$\begin{matrix}{{\hat{H}}_{2} = {{{{- t}{\sum\limits_{\langle{p,q}\rangle}{{\hat{c}}_{p}^{\dagger}{\hat{c}}_{q}}}} + {\sum\limits_{p}{\upsilon_{p}{\hat{c}}_{p}^{\uparrow}{\hat{c}}_{p}}} + {H.C}}..}} & (1)\end{matrix}$Note that, in the equation (1) , <p, q> means the adjacent sites; t is atransfer; and a random potential is introduced by v_(p). Here, v_(p) isa random variable generated by:−V/2<υ_(p) <V/2  (2)It is possible to introduce the random potential by, for example, addingimpurity or introducing a lattice defect.

The Anderson localization occurs to cause an insulation state when V/tis sufficiently large, while a metallic Fermi liquid is constructed whenV/t is sufficiently small. It is known that all single electron statesare localized in an infinite two-dimensional system unless intensity ofthe random potential is zero no matter how weak the intensity is.However, since a length of the localization is finite, the systembehaves as if it is in the metallic state in the finite region so far asthe localization length is larger than the size of the system (La when adistance from a lattice point to an adjacent lattice point is a).

When intrinsic energy of Hamiltonian Ĥ₂ is ε_(m) and intrinsic vector ofHamiltonian is |m>, the following equation:Ĥ ₂ |m>=ε _(m) |m>  (3)is true. In the equation (3), m=0, 1, 2, or n.

To start with, an n+1 quantum level ε_(m) is standardized in such amanner that its average nearest level spacing becomes 1. That is to say,the following equation:w _(j)=ε_(j)−ε_(j-1)  (4)is used. When j=1, 2, or n in the equation (4), the quantum level isconverted into a new level: $\begin{matrix}{ɛ_{0} = 0} & (6) \\{ɛ_{m} = {{\frac{1}{\overset{\_}{\omega}}{\sum\limits_{j = 1}^{m}\omega_{j}}} = {\sum\limits_{j = 1}^{m}\Omega_{j}}}} & (7)\end{matrix}$using the following equation: $\begin{matrix}{\overset{\_}{\omega} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}{\omega_{j}.}}}} & (5)\end{matrix}$Here, the following equation: $\begin{matrix}{\Omega_{j} = \frac{\omega_{j}}{\overset{\_}{\omega}}} & (8)\end{matrix}$is true. The density of states of the system is defined by the followingequation: $\begin{matrix}{{{\rho(\varepsilon)} = {\frac{1}{n + 1}{\sum\limits_{m = 0}^{n}{\delta\left( {\varepsilon - ɛ_{m}} \right)}}}},} & (9)\end{matrix}$and the staircase function is calculated as follows: $\begin{matrix}{{\lambda(\varepsilon)} = {\int_{- \infty}^{\varepsilon}\quad{{\mathbb{d}\eta}\quad{{\rho(\eta)}.}}}} & (10)\end{matrix}$The thus-obtained staircase function is converted by using the operationcalled unfolding in such a manner that the density of states is constanton average. The thus-obtained quantum levels are used for calculating anearest level spacing distribution P(s) and Δ3 statistics of Dyson andMehta as quantum level statistics. As mentioned in Non-PatentLiteratures 12 and 13, the statistics are used for detecting whether ornot the quantum chaos is generated. It is known that the quantum chaossystem is sensitive to external perturbation as is the case with theclassical chaos system, and, therefore, the quantum chaos analysis isimportant as an index for nonlinear material designing.

In the case of the integrable system, the nearest level spacingdistribution P(s) and the Δ₃ statistics are well described as those ofthe Poisson distribution as follows: $\begin{matrix}{{P_{P}(s)} = {\mathbb{e}}^{- s}} & (11) \\{{\Delta_{3}(n)} = {\frac{n}{15}.}} & (12)\end{matrix}$In the case of the quantum chaos system, they are well described asthose of GOE (Gaussian orthogonal ensemble) distribution as follows:$\begin{matrix}{{P_{GOE}(s)} = {\frac{\pi s}{2}{\mathbb{e}}^{{- {\pi s}^{2}}/4}}} & (13) \\{{\Delta_{3}(n)} = {{\frac{1}{\pi^{2}}\left\lbrack {{\log\left( {2\pi\quad n} \right)} + \gamma - \frac{\pi^{2}}{8} - \frac{5}{4}} \right\rbrack} + {{O\left( n^{- 1} \right)}.}}} & (14)\end{matrix}$In the equations (13) and (14), γ is the Euler's constant. In thefollowing calculations, L is set to 40 (L=40) and a periodic boundarycondition is used. The total number of states is 1,600 (L²=1,600). Thequantum levels of from n=201 to n=800 are used. The quantum chaosproperty is controlled by fixing t to 1 (t=1) and adjusting V.

The nearest level spacing distribution P(s) is shown in FIG. 2, and theΔ3 statistics are shown in FIG. 3. V is set to 2, 6, 10, 14, 18, and 22.In the case of V=2, the quantum level statistics of the system are welldescribed as those of GOE and the system is in the metallic quantumchaos state. In the case of V=22, the quantum level statistics of thesystem are well described as those of the Poisson distribution and thesystem is in the Anderson localization state (the integrable system). Achange from the quantum chaos system to the integrable system along withthe change from V=2 to V=22 is observed.

The electron device which controls quantum chaos according to the firstembodiment will hereinafter be described. As shown in FIG. 4, two layersof the square lattice of which each side is L site are considered. Thetwo layers form a heterojunction. The maximum dimension of the layers({square root}2La when a distance between adjacent lattice points is a)is smaller than an electron coherence length. An operator: ĉ_(p) ^(t)for generating quantum is defined on a p-th lattice point of the firstlayer. An operator: {circumflex over (d)}_(p) ^(t) for generatingquantum is defined on a p-th lattice point of the second layer. Here,Hamiltonian Ĥ of the quantum system is defined by the followingequation: $\begin{matrix}\begin{matrix}{\hat{H} = {{{- t_{1}}{\sum\limits_{({p,q})}{{\hat{c}}_{p}^{t}{\hat{c}}_{q}}}} - {t_{2}{\sum\limits_{({p,q})}{{\hat{d}}_{p}^{t}{\hat{d}}_{q}}}} - {t_{3}{\sum\limits_{p}{{\hat{c}}_{p}^{t}{\hat{d}}_{p}}}} +}} \\{{\sum\limits_{p}{v_{p}{\hat{c}}_{p}^{t}{\hat{c}}_{p}}} + {\sum\limits_{p}{w_{p}{\hat{d}}_{p}^{t}{\hat{d}}_{p}}} + {\frac{\phi}{2}{\sum\limits_{p}\left( {{{\hat{c}}_{p}^{t}{\hat{c}}_{p}} - {{\hat{d}}_{p}^{t}{\hat{d}}_{p}}} \right)}} + {H.C.}}\end{matrix} & (15)\end{matrix}$In the equation (15), <p, q> means nearest sites in the layers; t₁ is atransfer of the first layer; t₂ is a transfer of the second layer; andt₃ is a transfer between the first layer and the second layer. A randompotential of the first layer is introduced by v_(p). Here, v_(p) is arandom variable generated by:−V ₁/2<v _(p) <V ₁/2  (16)A random potential of the second layer is introduced by w_(p). Here,w_(p) is a random variable generated by:−V ₂/2<w _(p) <V ₂/2  (17)

It is possible to introduce the random potentials by, for example,adding impurity or introducing a lattice defect.

In this case, one of the first layer and the second layer serves as aregion having an electron system characterized by quantum chaos and theother serves as a region having an electron system characterized byintegrability depending on the values of V₁/t₁ and V₂/t₂. For example,when V₁/t₁<V₂/t₂, the first layer serves as the region having theelectron system characterized by quantum chaos and the second layerserves as the region having the electron system characterized byintegrability.

Electrodes are provided under the first layer and on the second layer,and each of the electrodes having the size which is large enough tocover whole surface of the layer. By applying a voltage between theelectrodes, an electric field in a direction of z-axis is applieduniformly in such a manner as to penetrate the layers.

In the case of t₃=0, which is the simplest case wherein the first layerand the second layer are separated from each other, the first layer isin the state of metallic Fermi liquid when V₁/t₁ is sufficiently small,while the Anderson localization occurs in the second layer so that thesecond layer is in the insulation state when V₂/t₂ is sufficientlylarge.

In the case of t₃>0, the two layers form a quantum junction. An averagepotential difference φ between the two layers is introduced, and thisparameter is in proportion to intensity of the electric fieldpenetrating the layers. Changes in the quantum state of the system usingφ as the parameter are important.

In the following calculations, L is set to 40 (L=40) and a periodicboundary condition is used for each of the layers. The total number ofstates is 3,200 (2L²=3,200). Intrinsic energy values are obtained bydinagonalization, and quantum level statistics are calculated from theabove-described method. The quantum levels of from n=201 to n=800 areused. The quantum chaos property is controlled by fixing the values oft₁, t₂, t₃, V₁, and V₂ as follows: t₁=t₂=1; t₃=0.5; V₁=2; and V₂=20 aswell as by adjusting the value of φ.

Shown in FIG. 5 is a nearest level spacing distribution P(s), and shownin FIG. 6 is Δ3 statistics. The values used for φ are −4, −2.4, −0.8,0.8, 2.4, and 4. When φ is −4, electrons with large amplitude arepresent in the first layer having lower potential energy. In this case,the electrons are in the quantum chaos state which is well described bythe GOE distribution. Along with the increase in φ, amplitude in thesecond layer having a violent scattering due to the random potential isincreased and the quantum level statistics are changed. When (φ=4, theelectrons with large amplitude are present in the second layer havinglower potential energy to cause the Anderson localization in accordancewith the Poisson distribution which is integrable.

From the above analysis, it is apparent that the quantum chaos propertyof the quantum system is controlled owing to changes in value of φ,i.e., owing to changes in intensity of the electric field penetratingthe two layers.

In addition, in Non-Patent Literatures 10 and 11, Sakaki et al. discussswitching between the Anderson localization state and the metallic stateonly in terms of conductivity.

A specific example of the electron device which controls quantum chaosaccording to the first embodiment is shown in FIG. 7. Referring to FIG.7, in the electron device which controls quantum chaos, a crystal layer11 as the first layer and a crystal layer 12 as the second layer arequantum-mechanically bonded with each other with a crystal layer 13 as atunnel barrier being sandwiched therebetween to form a heterojunction.The crystal layer 11 as the first layer is undoped and high in purity,while the crystal layer 12 as the second layer is doped with a highconcentration ((1 to 2)×10¹⁸ cm⁻³, for example) of impurity. Anelectrode 15 is formed on a bottom face of the crystal layer 11 with aninsulating film 14 being formed therebetween, and an electrode 17 isformed on a top face of the crystal layer 12 with an insulating film 16being formed therebetween.

It is possible to produce the electron device which controls quantumchaos by, for example, the following process. As shown in FIG. 8A, thecrystal layers 11, 13, and 12 are grown in this order on a substrate 18.Examples of usable crystal growth method may be the metal organicchemical vapor deposition (MOCVD), the molecular beam epitaxy (MBE), andthe like. The crystal layer 12 is doped with impurity which is in anamount necessary for the crystal growth. The insulating film 16 isformed on the crystal layer 12, and an electroconductive film such as ametal film is formed on the insulating film 16 to form the electrode 17on the electroconductive film. Then, referring to FIG. 8B, the substrate18 is removed by polishing from the bottom face. Referring to FIG. 8C,the insulating film 14 is formed under the thus-exposed crystal layer11, and an electroconductive film such as a metal film is formed underthe insulating film 14 to form the electrode 15 on the electroconductivefilm. Then, the stacked structure is patterned to be in a predeterminedshape by lithography and etching. Thus, the electron device whichcontrols quantum chaos shown in FIG. 7 is obtained.

Specific examples of usable materials are as follows: an undoped GaAslayer is used for the crystal layer 11; an Si doped GaAs layer is usedfor the crystal layer 12; an undoped AlGaAs layer (Al composition is0.3, for example) is used for the crystal layer 13; an SiO₂ film is usedfor the insulating films 14 and 16, an Al film is used for theelectrodes 15 and 17; and a semi-insulation GaAs substrate is used forthe substrate 18.

Shown in FIG. 9 is another example of the electron device which controlsquantum chaos according to the first embodiment. Referring to FIG. 9, inthe electron device which controls quantum chaos, a crystal layer 21 asthe first layer and a crystal layer 22 as the second layer arequantum-mechanically bonded with each other with a crystal layer 23 as atunnel barrier being sandwiched therebetween to form a heterojunction.The lattice defect does not substantially exist in the crystal layer 21serving as the first layer (or there is a remarkably small amount oflattice defect), and an amount of the lattice defect in the crystallayer 22 serving as the second layer is at least larger than that of thecrystal layer 21. Under the crystal layer 21, a crystal layer 24 as aspacer layer, a crystal layer 25 as an electron supplying layer, and acrystal layer 26 as an insulating layer are stacked in this order, whilea crystal layer 27 as an insulating layer is stacked on the crystallayer 22. An electrode 28 is formed on a bottom face of the crystallayer 26, while an electrode 29 is formed on a top face of the crystallayer 27.

Since a manufacturing process of the electron device which controlsquantum chaos is almost the same as that of the electron device whichcontrols quantum chaos shown in FIG. 7, description thereof is omitted.

Specific examples of usable materials are as follows: an undoped GaAslayer is used for the crystal layers 21 and 22; an undoped AlGaAs layer(Al composition is 0.3, for example) is used for the crystal layers 23,24, 26, and 27; an Si doped AlGaAs layer (Al composition is 0.3, forexample) is used for the crystal layer 25; and an Al film is used forthe electrodes 28 and 29.

In the electron device which controls quantum chaos of FIG. 9, thesystem behaves as a metal when the electrons supplied from the crystallayer 25 are present in the crystal layer 21 having no lattice defect,and the system behaves as if it is in the metallic state transitions tothe Anderson localization phase when the electrons are attracted to thecrystal layer 22 having lattice defect due to the potential differencebetween the electrodes 28 and 29.

As described in the foregoing, according to the first embodiment, theheterojunction is formed by bonding the region having the electronsystem characterized by quantum chaos with the region having theelectron system characterized by integrability, and the electric fieldperpendicular to the junction surface is applied to the heterojunctionto externally and extensively control the quantum chaos property of theelectron system in the system formed of the regions in such simplemanner. Further, it is possible to form the heterojunction simply byusing a single material.

Second Embodiment

An electron device which controls quantum chaos according to the secondembodiment uses a heterojunction which is a junction system of a regionhaving an electron system characterized by quantum chaos and a regionhaving an electron system characterized by integrability, and magneticimpurity is particularly used as impurity for introducing a randompotential in this case.

Before describing the second embodiment, electrons on a two-dimensionalsquare lattice, more specifically an electron state in a two-dimensionalrandom potential, will be described.

As shown in FIG. 1, each side of the square lattice is L site. Anoperator ĉ_(p) ^(t) for generating quantum is defined on a p-th latticepoint of the square lattice. Here, Hamiltonian Ĥ₂ of a quantum system isdefined as follows: $\begin{matrix}{{\hat{H}}_{2} = {{{- {\sum\limits_{\langle{p,q}\rangle}{t_{p,q}{\hat{c}}_{p}^{\dagger}{\hat{c}}_{q}}}} + {\sum\limits_{p}{\upsilon_{p}{\hat{c}}_{p}^{\uparrow}{\hat{c}}_{p}}} + {H.C}}..}} & (18)\end{matrix}$In the equation (18), <p, q> means the adjacent sites, and the randompotential is introduced by v_(p). Here, v_(p) is a random variablegenerated by:−V/2<υ_(p) <V/2  (19)It is possible to introduce the random potential by, for example, addingimpurity or introducing a lattice defect. The transfer t_(p,q) isdefined by the following equation:t_(p,q)=exp(2πiθ_(p,q))  (20)wherein θ_(p,q) satisfies θ_(p,q)=−θ_(p,q) and is a random variablegenerated by |θ_(p,q)|<ξ/2. A random magnetic field is introduced whenξ>0 is satisfied.

The Anderson localization occurs to cause an insulation state when V issufficiently large, while a metallic Fermi liquid is constructed when Vis sufficiently small. As mentioned in the foregoing, it is known thatall single electron states are localized in an infinite two-dimensionalsystem unless intensity of the random potential is zero no matter howweak the intensity is. However, since a length of the localization isfinite, the system behaves as if it is in the metallic state in thefinite region when the localization length is larger than the size ofthe system La.

When intrinsic energy of Hamiltonian Ĥ₂ is ε_(m) and an intrinsic vectorof Hamiltonian is |m>, the following equation:Ĥ₂|m>=ε_(m)|m>  (21)is derived. In the equation (21), m=0, 1, 2, or n.

To start with, an n+1 quantum level ε_(m) is standardized in such amanner that its average nearest level spacing becomes 1. That is to say,the following equation:w _(j)=ε_(j)−ε_(j-1)  (22)is true. When j=1, 2, or n, the quantum level is converted into a newlevel: $\begin{matrix}{ɛ_{0} = 0} & (24) \\{ɛ = {{\frac{1}{\overset{\_}{\omega}}{\sum\limits_{j = 1}^{m}\omega_{j}}} = {\sum\limits_{j = 1}^{m}\Omega_{j}}}} & (25)\end{matrix}$using the following equation: $\begin{matrix}{\overset{\_}{\omega} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}{\omega_{j}.}}}} & (23)\end{matrix}$Here, the following equation: $\begin{matrix}{\Omega_{j} = \frac{\omega_{j}}{\overset{\_}{\omega}}} & (26)\end{matrix}$is used. The density of states of the system is defined by the followingequation: $\begin{matrix}{{{\rho(\varepsilon)}\frac{1}{n + 1}{\sum\limits_{m = 0}^{n}{\delta\left( {\varepsilon - ɛ_{m}} \right)}}},} & (27)\end{matrix}$and the staircase function is calculated as follows: $\begin{matrix}{{\lambda(\varepsilon)} = {\int_{- \infty}^{\varepsilon}\quad{{\mathbb{d}\eta}\quad{{\rho(\eta)}.}}}} & (28)\end{matrix}$The thus-obtained staircase function is converted by employing theoperation called unfolding in such a manner that the density of statesis constant on average. The thus-obtained quantum level is used forcalculating a nearest level spacing distribution P(s) and Δ3 statisticsof Dyson and Mehta as quantum level statistics. As mentioned in theforegoing, the statistics are used for detecting whether or not thequantum chaos is generated.

In the case of the integrable system, the nearest level spacingdistribution P(s) and the Δ₃ statistics are well described as those ofthe Poisson distribution as follows: $\begin{matrix}{{P_{p}(s)} = {\mathbb{e}}^{- s}} & (29) \\{{\Delta_{3}(n)} = {\frac{n}{15}.}} & (30)\end{matrix}$In the case of the quantum chaos system, they are well described asthose of GUE (Gaussian unitary ensemble) distribution as follows:$\begin{matrix}{{P_{GUE}(s)} = {\frac{32s^{2}}{\pi^{2}}{\mathbb{e}}^{{- 4}{s^{2}/\pi}}}} & (31) \\{{\Delta_{3}(n)} = {{\frac{1}{2\pi^{2}}\left\lbrack {{\log\left( {2\pi\quad n} \right)} + \gamma - \frac{5}{4}} \right\rbrack} + {{O\left( n^{- 1} \right)}.}}} & (32)\end{matrix}$In the equations (31) and (32) γ is the Euler's constant.

In the following calculations, L is set to 60 (L=60) and a periodicboundary condition is used. The total number of states is 3,600(L²=3,600). The quantum levels of from n=201 to n=1,800 are used. Thequantum chaos property is controlled by fixing ξ to 0.1 (ξ=0.1) andadjusting V.

The nearest level spacing distribution P(s) is shown in FIG. 10, and theΔ3 statistics are shown in FIG. 11. Values used for V are 2, 6, 10, 14,18, and 22. In the case of V=2, the quantum level statistics ofthesystem are approximately described as those of GUE and the system is inthe metallic quantum chaos state. In a closer observation, a shift fromthe quantum chaos system is observed. Since the system istwo-dimensional, such shift is caused by the influence of the Andersonlocalization. In the case of V=22, the quantum level statistics of thesystem are well described as those of Poisson distribution, and thesystem is in the Anderson localization state (the integrable system). Achange from the quantum chaos system to the integrable system along withthe change from V=2 to V=22 is observed.

The electron device which controls quantum chaos according to the secondembodiment will hereinafter be described.

As shown in FIG. 4, two layers of square lattice wherein each side is Lsite are considered as in the first embodiment. The two layers form aheterojunction. The maximum dimension of the layers ({square root}2Lawhen a distance between adjacent lattice points is a) is equal to orless than an electron coherence length. An operator ĉ_(p) ^(t) forgenerating quantum is defined on a p-th lattice point of the firstlayer. An operator {circumflex over (d)}_(p) ^(t) for generating quantumis defined on a p-th lattice point of the second layer. Here,Hamiltonian Ĥ of the quantum system is defined by the followingequation: $\begin{matrix}\begin{matrix}{\hat{H} = {{- {\sum\limits_{({p,q})}{t_{p,q}^{(1)}{\hat{c}}_{p}^{t}{\hat{c}}_{q}}}} - {\sum\limits_{({p,q})}{t_{p,q}^{(2)}{\hat{d}}_{p}^{t}{\hat{d}}_{q}}} - {\sum\limits_{p}{t_{p}^{(3)}{\hat{c}}_{p}^{t}{\hat{d}}_{p}}} +}} \\{{\sum\limits_{p}{v_{p}{\hat{c}}_{p}^{t}{\hat{c}}_{p}}} + {\sum\limits_{p}{w_{p}{\hat{d}}_{p}^{t}{\hat{d}}_{p}}} + {\frac{\phi}{2}{\sum\limits_{p}\left( {{{\hat{c}}_{p}^{t}{\hat{c}}_{p}} - {{\hat{d}}_{p}^{t}{\hat{d}}_{p}}} \right)}} + {H.C.}}\end{matrix} & (33)\end{matrix}$In the equation (33), <p, q> means nearest sites in each of the layers.A random potential of the first layer is introduced by v_(p). Here,v_(p) is a random variable generated by:−V ₁/2<v _(p) <V ₁/2  (34)A random potential of the second layer is introduced by w_(p). Here,w_(p) is a random variable generated by:−V ₂/2<w _(p) <V ₂/2  (35)It is possible to introduce the random potentials by, for example,adding impurity or introducing a lattice defect. The transfers t_(p,q)⁽¹⁾, t_(p,q) ⁽²⁾, t_(p) ⁽³⁾ are represented by the following equations:t _(p,q) ⁽¹⁾ =t ₁ exp(2πiθ _(p,q) ⁽¹⁾)  (36)t _(p,q) ⁽²⁾ =t ₂ exp(2πiθ _(p,q) ⁽²⁾)  (37)t _(p) ⁽³⁾ =t ₃ exp(2πiθ _(p) ⁽³⁾)  (38)The transfers satisfy the following equations:θ_(p,q) ⁽¹⁾=−θ_(q,p) ⁽¹⁾, θ_(p,q) ⁽²⁾=−θ_(q,p) ⁽²⁾and are random variables generated by:|θ_(p,q) ⁽¹⁾|<ξ/2, |θ_(p,q) ⁽²⁾|<ξ/2, |θ_(p) ⁽³⁾|<ξ/2A random magnetic field is introduced when ξ>0 is satisfied.

In the case of t₃=0, which is the simplest case wherein the first layerand the second layer are separated from each other, the first layer isin the metallic Fermi liquid state when V₁/t₁ is sufficiently small,while the Anderson localization occurs in the second layer so that thesecond layer is in the insulation state when V₂/t₂ is sufficientlylarge.

In the case of t₃>, the two layers form a quantum junction. An averagepotential difference φ between the two layers is introduced, and thisparameter is in proportion to intensity of the electric fieldpenetrating the layers. Changes in the quantum state of the system usingφ as the parameter are important.

In the following calculations, L is set to 60 (L=60) and a periodicboundary condition is used for each of the layers. The total number ofstates is 7,200 (2L²=7,200). Intrinsic energy values are obtained bydinagonalization, and quantum level statistics are calculated from theabove-described method. The quantum levels of from n=201 to n=1,800 areused. The quantum chaos property is controlled by fixing the values oft₁, t₂, t₃, V₁, V₂, and ξ, as follows: t₁=t₂=1; t₃=0.5; V₁=1; V₂=12; andξ=0.1 as well as by adjusting the value of φ.

Shown in FIG. 12 is a nearest level spacing distribution P(s), and shownin FIG. 13 is Δ3 statistics. The values used for φ are −4, −2.4, −0.8,0.8, 2.4, and 4. When φ is −4, electrons with large amplitude arepresent in the first layer having lower potential energy. In this case,the electrons are in the quantum chaos state which is well described bythe GUE distribution. Along with the increase in φ, amplitude in thesecond layer, which has a violent scattering due to the randompotential, is increased to change the quantum level statistics. Whenφ=4, the electrons with large amplitude are present in the second layerhaving lower potential energy to cause the Anderson localization inaccordance with the Poisson distribution which is integrable.

From the above analysis, it is apparent that the quantum chaos propertyof the quantum system is controlled owing to the changes in value of φ,i.e., owing to the changes in intensity of the electric fieldpenetrating the two layers.

Other parts of this embodiment are the same as those of the firstembodiment.

As described above, according to the second embodiment, theheterojunction is formed by bonding the region having the electronsystem characterized by quantum chaos with the region having theelectron system characterized by integrability and by adding themagnetic impurity for the introduction of random potential, and theelectric field perpendicular to the junction surface is applied to theheterojunction to externally and extensively control the quantum chaosproperty of the electron system in the system formed of the regions insuch simple manner. Further, it is possible to form the heterojunctionsimply by using a single material.

Third Embodiment

An electron device which controls quantum chaos according to the thirdembodiment uses a heterojunction which is a junction system of a regionhaving an electron system characterized by quantum chaos and a regionhaving an electron system characterized by integrability, and a Fermilevel of an electron system is used for the control on quantum chaosproperty in addition to the changes in electric field intensity in thiscase.

Constitution of this electron device which controls quantum chaos is thesame as that of the electron device which controls quantum chaos of thefirst embodiment except that the Fermi level of the electron system isset to a predetermined value.

Quantum level statistics are calculated by the method described in thefirst embodiment. In the following calculations, L is set to 80 (L=80)and a periodic boundary condition is used for each of the layers. Thetotal number of states is 12,800 (2L²=12,800). Intrinsic energy valuesare obtained by dinagonalization to calculate the quantum levelstatistics. In the following calculations, the quantum chaos property iscontrolled by fixing the values of t₁, t₂, t₃, V₁ and V₂, as follows:t₁=t₂=1; t₃=0.5; V₁=2; and V₂=20 as well as by adjusting the value of φ.

The quantum levels of from n=201 to n=3,200 are used. Shown in FIG. 14is a nearest level spacing distribution P(s), and shown in FIG. 15 is Δ3statistics. The values used for φ are −6, −3.6, −1.2, 1.2, 3.6, and 6.When φ=6, electrons with large amplitude are present in the second layerhaving lower potential energy to cause the Anderson localization inaccordance with the Poisson distribution which is integrable. Along withthe decrease in φ, amplitude in the first layer with relatively weakscattering which is caused by the random potential is increased tochange the quantum level statistics. When φ=−6, the first layer is in ametallic quantum chaos state which is well described by the GOEdistribution.

From the above analysis, it is apparent that the quantum chaos propertyof the quantum system is controlled by the changes in φ, i.e., thechanges in intensity of the electric field penetrating the two layers.

In order to quantitatively investigate the modulation in quantum chaosproperty, the Berry-Robnik parameter ρ is introduced (Non-PatentLiterature 14). When {overscore (ρ)}=1−ρ, the following equation:$\begin{matrix}{{P_{2}\left( {s,\rho} \right)} = {{\rho^{2}{\mathbb{e}}^{{- \rho}\quad s}{{erf}\left( \frac{\sqrt{\pi}\overset{\_}{\rho}\quad s}{2} \right)}} + {\left( {{2\rho\overset{\_}{\rho}} + \frac{\pi{\overset{\_}{\rho}}^{3}s}{2}} \right){\mathbb{e}}^{{{- \rho}\quad s} - {\pi_{\rho}^{- 2}{s^{2}/4}}}}}} & (39)\end{matrix}$is introduced. In the equation (39), the following equation:$\begin{matrix}{{{erf}(x)} = {\frac{2}{\sqrt{\pi}}{\int_{x}^{\infty}\quad{{\mathbb{d}\tau}\quad{\mathbb{e}}^{- r^{2}}}}}} & (40)\end{matrix}$is used. The function P₂ (s,p) coincides with P(s) of the Poissondistribution when p=1 and coincides with P(s) of the GOE distributionwhen p=0. That is to say, it is possible to interpolate the quantumlevel statistics from the quantum chaos system to the integrable systemby changing the value of p from 0 to 1. The Berry-Robnik parameter isthe value of p when P(s) which is obtained by the mathematicalcalculation is approximated by using P₂(s,p). In the scope of thesemi-classical approximation, p is a volume ratio of a regular region (aregion including the integrable system and a region generated bysubjecting the integrable system to a perturbation expansion) in a phasespace (Non-Patent Literature 15). Therefore, in the Andersonlocalization system discussed herein, p is regarded as a volume ratio ofthe localization state.

Shown in FIG. 16 is the Berry-Robnik parameter in the above-describedsystem. The Berry-Robnik parameter is increased in value in the regionwhere φ is large to indicate that a degree of the localization is great.The Berry-Robnik parameter value is reduced with the reduction in φ andreaches about 0 when φ is −2, thereby indicating that the system has thequantum chaos property.

These data reveal average characteristics relating to the wide energyregion of from n=201 to n=3,200.

In order to control the quantum chaos by setting the Fermi level of theelectron system to a predetermined value, it is necessary to studyenergy dependence of the quantum level statistics. Shown in FIG. 17 areBerry-Robnik parameters obtained by calculating the quantum levelstatistics using 1,000 states of from n=201 to n=1,200; the Berry-Robnikparameters obtained by the calculation using 1,000 states of fromn=1,201 to n=2,200; and the Berry-Robnik parameters obtained by thecalculation using 1,000 states of from n=2,201 to n=3,200. As isapparent from the three examples, in the case of the analysis of therelatively low energy state of 201 to 1,200, the obtained Berry-Robnikparameters are increased in value when the value of φ is relativelysmall to show the quantum localization property. The value of φ at whichthe Anderson transition occurs is larger in the energy state of 1,201 to2,200, and this tendency is more conspicuous in the energy state of2,201 to 3,200.

When the above results are applied to the electron system, a response ofthe electron system when the Fermi level of the electron system of thesystem is positioned at a point between n=201 and n=1,200 by controllinga voltage to be applied between the electrodes is well described by thedata of from 201 to 1,200 shown in FIG. 17. Also, a response of theelectron system when the Fermi level of the electron system of thesystem is positioned at a point between n=1,201 and n=2,200 is welldescribed by the data of from 1,201 to 2,200 shown in FIG. 17. Further,a response of the electron system when the Fermi level of the electronsystem of the system is positioned at a point between n=2,201 andn=3,200 is well described by the data of from 2,201 to 3,200 shown inFIG. 17. Thus, the tendency toward localization is greater in the lowenergy state, and it is apparent that the critical potential with whichthe Anderson transition occurs due to the electric field effect, i.e.the electric field intensity, is controlled by controlling the Fermilevel of the electron system.

Other parts of this embodiment are the same as those of the firstembodiment.

As described in the foregoing, according to the third embodiment, theheterojunction is formed by bonding the region having the electronsystem characterized by quantum chaos with the region having theelectron system characterized by integrability, and the Fermi level ofthe electron system of the system formed of the regions is set to apredetermined value by controlling the density of the electron system inaddition to the application of the electric field perpendicular to thejunction surface to the heterojunction, thereby externally andextensively controlling the quantum chaos property of the electronsystem in the system in such simple manner. Further, it is possible toform the heterojunction simply by using a single material.

Fourth Embodiment

An electron device which controls quantum chaos according to the fourthembodiment uses a heterojunction which is a junction system of a regionhaving an electron system characterized by quantum chaos and a regionhaving an electron system characterized by integrability, and a transferbetween the regions is set to a value smaller than that of each of theregions in this case to cause the Anderson transition accompanyingquantum chaos to occur rapidly.

Constitution of the electron device which controls quantum chaos is thesame as that of the electron device which controls quantum chaos of thefirst embodiment except that the transfers are set in the abovedescribed manner.

Quantum level statistics are calculated by the method described in thefirst embodiment, and Berry-Robnik parameter ρ is introduced in order toquantitatively investigate the modulation in quantum chaos property. Inthe following mathematical calculations, L is set to 80 (L=80) and aperiodic boundary condition is used for each of the layers. The totalnumber of states is 12,800 (2L²=12,800). Intrinsic energy values areobtained by dinagonalization to calculate the quantum level statistics.In the following calculations, the quantum chaos property are controlledby fixing the values of t₁, t₂, t₃, V₁, and V₂ as follows: t₁=t₂=1;t₃=½, 1, 2, 4, and 8; V₁=2; and V₂=20 as well as by adjusting the valueof φ. The quantum levels of from n=1,201 to n=3,200 are used. Shown inFIG. 18 is the Berry-Robnik parameter. Referring to FIG. 18, in the caseof t₃=½, the obtained Berry-Robnik parameter is large at a region whereφ is large to show the great localization property. The Berry-Robnikparameter is reduced with the reduction in φ and p reaches about 0 whenφ=−2 where system shows the quantum chaos property. With the increase int₃, the modulation is reduced. Particularly, when t₃=4 or more, thefunction for φ changes to be more linear.

The Anderson transition in an infinite system will hereinafter bereviewed. In a pure two-dimensional system, all single electron quantumstates are localized at the absolute zero so that the system alwaysbehaves as an insulator unless intensity of the random potential is zerono matter how weak the intensity is. Conductivity occurs at a finitetemperature since the coherence length is infinite at the finitetemperature; however, it is known that correction item of conductivityby quantum phase interference effect in a region having a weak randompotential (weak localization region) does not dependon the randompotential intensity. In terms of the system of this embodiment, when t₃is sufficiently large, the bonding state and the antibonding state ofthe first layer and the second layer are sufficiently separated. In thiscase, the bonding state when the Fermi level is positioned at thebonding state, for example, is considered to be the pure two-dimensionalquantum limit. The random potential intensity is modulated by theelectric field effect, but it is assumed from the above discussion thatthe modulation has less influence on the electron state. The quantumstates of the first layer and the second layer are mixed with each otheralong with the reduction in t₃ so that the pure two-dimensional systemis lost, thereby causing rapid metal/insulator phase transition. In thiscase, each of the values of t₁ and t₂ is 1. Therefore, a bandwidth ofeach of the layers is 4, and the rapid Anderson transition occurs whent₃ is sufficiently smaller than the bandwidth.

Analysis by the inverse participation ratio will hereinafter beexplained.

The inverse participation ratio which has frequently been used in theanalysis of Anderson transition is a quantity described as follows$\begin{matrix}{\alpha_{m} = {\sum\limits_{r}{{{\phi_{m}(r)}}^{4}.}}} & (41)\end{matrix}$In the equation (41), φm(r) is a wave function of the intrinsic energyε_(m), and r represents a lattice point. More specifically, the fourthpower of the wave function of the m-th energy intrinsic state issubjected to a space integration to obtain the inverse participationratio. When the random potential intensity is spatially constant, theAnderson transition in the system is clarified by analyzing thequantity. The reasons for the above are briefly given below.$\begin{matrix}{{\phi_{m}(r)} = \left\{ \begin{matrix}{{1/\sqrt{\omega}}\quad} & {{{when}\quad r} \in \Omega} \\{0\quad} & {otherwise}\end{matrix} \right.} & (42)\end{matrix}$is considered as the wave function as a typical example of thelocalization state, whose volume is localized in a region Ω having avolume of ω. In this case, the inverse participation ratio is$\begin{matrix}{\alpha_{m} = {{\int_{\Omega}\quad{{\mathbb{d}V}\frac{1}{\omega^{2}}}} = {\frac{1}{\omega}.}}} & (43)\end{matrix}$Therefore, the quantity is in inverse proportion to the localized volumeand is asymptotic to zero in the metallic state.

The quantity will be calculated in this system as follows. In thecalculation, L is set to 40 (L=40), and the total number of states is3,200 (N=2×40²). Since α_(m) itself is distributed, it is convenient toanalyze the quantity by defining the quantity as a quantity averaged inan energy window.

The following equation: $\begin{matrix}{{\alpha\left( {E,W} \right)} = {\frac{1}{\mu\left( {E,W} \right)}{\sum\limits_{m \in {\Omega{({E,W})}}}\alpha_{m}}}} & (44)\end{matrix}$is introduced. In the equation (44),Ω(E,W)={m|E−W/2<ε_(m) <E+W/2}  (45)That is to say, the intrinsic energy value ε_(m) is in the rage of Wwith the center being E, and the number of states is written as μ(E, W).Here, the value used for W is 0.4.

The quantities in the cases where t₃=½, t₃=1, t₃=2, t₃=4, and t₃=8 areshown in FIGS. 19, 20, 21, 22, and 23. In these graphs, the values usedfor φ are −6, −4, −2, 0, 2, 4, and 6. The values for φ are indicated oneach of the graphs as being shifted by 0.4 in the vertical direction. Aregion in which α(E, W) is almost zero is present in FIG. 19 where therapid phase transition is observed, and the region shifts with φ togenerate the metal/insulator phase transition. In the case where t₃ islarge, the region in which α(E, W) is almost zero is absent, andtendency of being always localized is observed in all energy regions.This can be considered as an effect of the two-dimensional quantumlimit.

A specific example of an electron device which controls quantum chaos asa physical system having a small t₃ is shown in FIG. 24.

Referring to FIG. 24, in the electron device which controls quantumchaos, an insulating layer 31 formed from undoped AlGaAs or the like, alocalization layer 32 formed from GaAs or the like, a tunnel barrier 33formed from undoped AlGaAs or the like, a conductive, layer 34 formedfrom undoped AlGaAs or the like, and an insulating layer 35 formed fromundoped AlGaAs or the like are stacked in this order to form aheterojunction of AlGaAs/GaAs/AlGaAs/AlGaAs/AlGaAs (in the order of frombottom to top). In the localization layer 32, a random potential isintroduced by adding thereto impurity or introducing thereto a latticedefect, and the random potential is not introduced to other layers or,if introduced, the quantity is ignorable. The localization layer 32 maybe an undoped layer when the random potential introduction is performedthrough the lattice defect introduction. The localization layer 32 showsAnderson localization, and the conductive layer 34 shows the metallicstate. An Al composition of AlGaAs of the conductive layer 34 isselected in such a manner that energy at the bottom (lower end) of aconductive band of the conductive layer 34 is a little higher than thatof the localization layer 32 and is sufficiently lower than those of thetunnel barrier 33 and the insulating layer 35. Electrodes (not shown)are formed on the insulating layer 35 and a bottom face of theinsulating layer 31, and it is possible to apply an electric field inthe z-axis direction by applying a voltage between the electrodes.

Shown in FIG. 25 is an energy band perpendicular to a hetero surface ofthe electron device which controls quantum chaos. Referring to FIG. 25,E_(c) represents the energy at the bottom of the conductive band andE_(v) represents energy on the top (upper end) of a valence band (thesame applies to other diagrams).

As described in the foregoing, according to the fourth embodiment, theheterojunction is formed by bonding the region having the electronsystem characterized by quantum chaos with the region having theelectron system characterized by integrability, and the transfer betweenthe regions is set to a value smaller than the transfer of each of theregions, preferably set to a value small enough, thereby making itpossible to externally and extensively control the quantum chaosproperty of the electron system formed of the regions and the Andersontransition in the system as well as to cause the Anderson transitionrapidly by such simple manner of applying to the heterojunction anelectric field perpendicular to the junction surface. Further, it ispossible to form the heterojunction simply by using a single material.

Fifth Embodiment

An electron device which controls quantum chaos according to the fifthembodiment is obtained by using a double heterojunction which is ajunction system of a region having an electron system characterized byquantum chaos and regions each having an electron system characterizedby integrability and being disposed on each sides of the region havingthe electron system characterized by quantum chaos.

Shown in FIG. 26 are three layers of square lattice wherein each side isL site. The double heterojunction is formed of these three layers. Amaximum dimension of the layers is smaller than an electron coherencelength ({square root}2La when a distance between adjacent lattice pointsis a). An operator ĉ_(p) ^(t) for generating quantum is defined on ap-th lattice point of the first layer. An operator {circumflex over(d)}_(p) ^(t) for generating quantum is defined on a p-th lattice pointof the second layer. An operator ê_(p) ^(t) for generating quantum isdefined on a p-th lattice point of the third layer. Here, Hamiltonian Ĥof the quantum system is defined by the following equation:$\begin{matrix}{\hat{H} = {{{{- t_{1}}{\sum\limits_{({p,q})}{{\hat{c}}_{p}^{\dagger}{\hat{c}}_{q}}}} - {t_{2}{\sum\limits_{({p,q})}{{\hat{d}}_{p}^{\dagger}{\hat{d}}_{q}}}} - {t_{3}{\sum\limits_{({p,q})}{{\hat{e}}_{p}^{\dagger}{\hat{e}}_{q}}}} - \quad{t_{12}{\sum\limits_{p}{{\hat{c}}_{p}^{\dagger}{\hat{d}}_{p}}}} - {t_{2S}{\sum\limits_{p}{{\hat{d}}_{p}^{\dagger}{\hat{e}}_{p}}}} + {\sum\limits_{p}{u_{p}{\hat{c}}_{p}^{\dagger}{\hat{c}}_{p}}} + \quad{\sum\limits_{p}{v_{p}{\hat{d}}_{p}^{\dagger}{\hat{d}}_{p}}} + {\sum\limits_{p}{w_{p}{\hat{e}}_{p}^{\dagger}{\hat{e}}_{p}}} + {\frac{\phi}{2}{\sum\limits_{p}\left( {{{\hat{e}}_{p}^{\dagger}{\hat{e}}_{p}} - {{\hat{c}}_{p}^{\dagger}{\hat{c}}_{p}}} \right)}} + {H.C}}..}} & (46)\end{matrix}$In the equation (46), <p, q> means nearest sites in each of the layers;t₁ represents the transfer of the first layer; t₂ represents thetransfer of the second layer; t₃ represents the transfer of the thirdlayer; t₁₂represents the transfer between the first layer and the secondlayer; and t₂₃ represents the transfer between the second layer and thethird layer. A random potential of the first layer is introduced byu_(p). Here, u_(p) is a random variable generated by:−V ₁/2<u _(p) <V ₁2  (47)A random potential of the second layer is introduced by v_(p). Here,v_(p) is a random variable generated by:−V ₂/2<V _(p) <V ₂2  (48)A random potential of the third layer is introduced by w_(p). Here,w_(p) is a random variable generated by:−V ₃/2<w _(p) <V ₃2  (49)It is possible to introduce the random potentials by, for example,adding impurity or introducing a lattice defect.

When t₁₂=0, the first layer and the second layer are separated from eachother. When t₂₃=0, the second layer and the third layer are separatedfrom each other. In the case where the three layers are separated fromone another, the j-th layer is in the metallic Fermi liquid state whenV_(j)/t_(j) is sufficiently small. On the other hand, in the case wherethe quantity is sufficiently large, the Anderson localization occurs sothat the system is in the insulation state.

When t₁₂>0 and t₂₃>0, the three layers form a quantum junction. Anaverage potential difference φ of the first and the third layers isintroduced, and this parameter is proportion to the electric fieldpenetrating the three layers. Changes in the quantum state of the systemusing φ as the parameter are important.

An inverse participation ratio is calculated in the same manner as inthe fourth embodiment. In the calculation, L is set to 40 (L=40), andthe total number of states is 4,800 (N=3×40²). Since the number ofstates μ(E, W) is in proportion to the density of states, the followingequation:D(E,W)=μ(E,W)/μ_(max)  (50)is introduced. For the purpose of standardization, the followingequation: $\begin{matrix}{\mu_{\max} = {\max\limits_{E}{\mu\left( {E,W} \right)}}} & (51)\end{matrix}$is introduced. The following calculations are conducted by using 0.4 asthe value of W.

In the following mathematical calculations, a periodic boundarycondition is used for each of the layers. Intrinsic energy values andintrinsic functions are obtained by the dinagonalization, and α(E,W) andD(E,W) are calculated. In the following calculations, definitions oft₁=t₂=t₃=1 and t₁₂=t₂₃=0.5 are used.

The cases of 1−α(E, W) and D(E, W) when V₁=2, V₂=20, and V₃=2 are shownin FIGS. 27 and 28. Values used for φ are −16, −12, −8, −4, 0, 4, 8, 12,and 16 in the figures. The system has the three layer structure ofconductive layer/localization layer/conductive layer. The layers areindicated as being shifted by 1.2 in the vertical direction. As isapparent form FIG. 27, a region in which 1−α(E, W)=about 1 is present.In this region, the metallic quantum state is observed. A rapidmetal/insulator phase transition occurs when the region moves with φ.Referring to FIG. 28, in the energy region where the metallic quantumstate is observed, the value of D(E,W) is large. In the double heteroticstructure, the metallic state appears on two points. Therefore, it isclarified that the three layer structure enables the quantum statecontrol in the more extensive electron system.

The cases of 1−α(E, W) and D(E, W) when V₁=20, V₂=2, and V₃=20 are shownin FIGS. 29 and 30 as complementary. In these cases, the system has athree-layer structure of localization layer/conductivelayer/localization layer. The energy region in which 1−α(E, W) becomessubstantially 1, i.e. the metallic quantum state, is present in the bandcenter. This region does not depend on φ since the conductive layerwhich takes the important roll in the metallic quantum state ispositioned on the center to be free from the influence of φ.

A specific example of an electron device which controls quantum chaoshaving the above-described three layer structure of conductivelayer/localization layer/conductive layer is shown in FIG. 31.

As shown in FIG. 31, in the electron device which controls quantumchaos, an insulating layer 41 formed from undoped AlGaAs or the like, aconductive layer 42 formed from undoped AlGaAs or the like, a tunnelbarrier 43 formed from undoped AlGaAs or the like, a localization layer44 formed from InGaAs or the like, a tunnel barrier 45 formed fromundoped AlGaAs or the like, a conductive layer 46 formed from undopedAlGaAs or the like, and an insulating layer 47 formed from undopedAlGaAs or the like are stacked in this order to form a heterojunction ofAlGaAs/AlGaAs/AlGaAs/InGaAs/AlGaAs/AlGaAs/AlGaAs (in the order of frombottom to top). In the localization layer 44, a random potential isintroduced by adding thereto impurity or introducing thereto a latticedefect, and the random potential is not introduced to other layers or,if introduced, the quantity is ignorable. The localization layer 44 maybe an undoped layer when the random potential introduction is performedthrough the lattice defect introduction. The localization layer 44 showsthe Anderson localization, and the conductive layers 42 and 46 show themetallic state. An Al composition of AlGaAs of each of the conductivelayers 42 and 46 is selected in such a manner that energy at the bottom(lower end) of a conductive band of each of the conductive layers 42 and46 is sufficiently lower than those of the tunnel barriers 43 and 45 andthe insulating layers 41 and 47. Electrodes (not shown) are formed onthe insulating layer 47 and a bottom face of the insulating layer 41,and it is possible to apply an electric field in the z-axis direction byapplying a voltage between the electrodes.

Shown in FIG. 32 is an energy band perpendicular to a hetero surface ofthe electron device which controls quantum chaos.

A specific example of an electron device which controls quantum chaoshaving the above-described three layer structure of localizationlayer/conductive layer/localization layer is shown in FIG. 33.

As shown in FIG. 33, in the electron device which controls quantumchaos, an insulating layer 51 formed from undoped AlGaAs or the like, alocalization layer 52 formed from InGaAs or the like, a tunnel barrier53 formed from undoped AlGaAs or the like, a conductive layer 54 formedfrom undoped AlGaAs or the like, a tunnel barrier 55 formed from undopedAlGaAs or the like, a localization layer 56 formed from InGaAs or thelike, and an insulating layer 57 formed from undoped AlGaAs or the likeare stacked in this order to form a heterojunction ofAlGaAs/InGaAs/AlGaAs/AlGaAs/AlGaAs/InGaAs/AlGaAs (in the order of frombottom to top). In each of the localization layers 52 and 56, a randompotential is introduced by adding thereto impurity or introducingthereto a lattice defect, and the random potential is not introduced toother layers or, if introduced, the quantity is ignorable. Thelocalization layers 52 and 56 may be undoped layers when the randompotential introduction is performed through the lattice defectintroduction. The localization layers 52 and 56 show the Andersonlocalization, and the conductive layer 54 shows the metallic state. AnAl composition of AlGaAs of the conductive layer 54 is selected in sucha manner energy at the bottom (lower end) of a conductive band of theconductive layer 54 is sufficiently lower than those of the tunnelbarriers 53 and 55 and the insulating layers 51 and 57. Electrodes (notshown) are formed on the insulating layer 57 and a bottom face of theinsulating layer 51, and it is possible to apply an electric field inthe z-axis direction by applying a voltage between the electrodes.

Shown in FIG. 34 is an energy band perpendicular to a hetero surface ofthe electron device which controls quantum chaos.

As described in the foregoing, according to the fifth embodiment, adouble heterojunction is formed by bonding regions each having theelectron system characterized by integrability with each sides of theregion having the electron system characterized by quantum chaos, andthe electric field perpendicular to the junction surfaces is applied tothe double heterojunction to externally and more extensively control thequantum chaos property of the electron system of the system formed ofthe regions in such simple manner. Further, it is possible to form theheterojunction simply by using a single material.

Sixth Embodiment

In the sixth embodiment, an example of an electron device which controlsquantum chaos which is manufactured by using a Ge material and has astacked structure shown in FIG. 31 as well as a manufacturing methodthereof will be described.

In this electron device which controls quantum chaos, an insulatinglayer 41 formed from undoped Si_(x)Ge_(1-x) (0<x<1) or the like, aconductive layer 42 formed from undoped Si_(y)Ge_(1-y) (0 ≦y<1) or thelike, a tunnel barrier 43 formed from undoped Si_(z)Ge_(1-z) (y<z<1) orthe like, a localization layer 44 formed from Ge which is doped withimpurity such as As, a tunnel barrier 45 formed from undopedSi_(z)Ge_(1-z) (y<z<1) or the like, a conductive layer 46 formed fromundoped Si_(y)Ge_(1-y) (0<y<1) or the like, and an insulating layer 47formed from undoped Si_(x)Ge_(1-x) (0<x<1) or the like are stacked inthis order in the lattice matching state to form a heterojunction ofSiGe/SiGe/SiGe/Ge/SiGe/SiGe/SiGe (in the order of from bottom to top). Arandom potential is introduced by adding As as impurity to Ge in thelocalization layer 44, and the random potential is not introduced toother layers or, if introduced, the quantity is ignorable. Thelocalization layer 44 shows the Anderson localization, and theconductive layers 42 and 46 show the metallic state.

Hereinafter, the method of manufacturing the electron device whichcontrols quantum chaos by employing the neutron transition doping (NTD)(Non-Patent Literature 16) will be described.

The NTD will be described in terms of Ge. Stable isotopes are present inGe, and abundance ratios of the isotopes are as follows: about 20% of⁷⁰Ge; about 27% of ⁷²Ge; about 8% of ⁷³Ge; about 37% of ⁷⁴Ge; and about8% of ⁷⁶Ge. Among the isotopes, ⁷⁰Ge, for example, causes a nuclearreaction due to a collision of neutrons to change into a stable nuclear⁷¹Ge by absorbing electrons. Also, ⁷⁴Ge causes a nuclear reaction withneutrons, and the nuclear reaction associates a β decay so that the ⁷⁴Geis changed into ⁷⁵As. Therefore, by exposing the Ge crystal containingthe isotopes to neutrons, the nuclear reactions are caused to enable aconversion of the Ge atoms in the crystal into atoms having nuclear suchas ⁷¹Ge and ⁷⁵As. According to this method, it is possible to perform adoping using the atoms without converting the atoms positioned on thelattice points of the crystal lattice. It is known that this methodenables a remarkably uniform doping.

In the manufacture of the electron device which controls quantum chaos,an undoped Si_(x) ⁷²Ge_(1-x) layer as the insulating layer 41, anundoped Si_(y) ⁷²Ge_(1-y) layer as the conductive layer 42, an undopedSi_(z) ⁷²Ge_(1-z) layer as the tunnel barrier layer 43, an undoped ⁷⁴Gelayer as the localization layer 44, an undoped Si_(z) ⁷²Ge_(1-z) layeras the tunnel barrier layer 45, an undoped Si_(y) ⁷²Ge_(1-y) layer asthe conductive layer 46, and an undoped Si_(z) ₇₂Ge_(1-z) layer as theinsulating layer 47 are stacked in this order on a predeterminedsubstrate (not shown) by the epitaxial growth.

Then, the thus-obtained stacked structure is irradiated with amonochromatic neutron beam having neutron energies which are uniform involume. As a result of the irradiation, ⁷⁴Ge which is a part of theundoped ⁷⁴Ge layer irradiated with the neutrons causes a nuclearreaction thanks to the neutron collision to convert into ⁷⁵As. Since theprobability of the nuclear reaction is in proportion to intensity of theincident neutron beam, ⁷⁵As is generated at a concentration proportionalto the incident neutron beam intensity. Since ⁷⁵As acts as n typeimpurity on the ⁷⁴Ge layer, the ⁷⁴Ge layer is doped with the n-typeimpurity ⁷⁵As as a result of the neutron irradiation. By adjusting theincident neutron beam intensity or the like, it is possible to control aconcentration of ⁷⁵As, i.e. a doping concentration, to achieve a desiredconcentration. Since Si⁷²Ge does not cause the nuclear reaction with theneutron beam irradiation, only the ⁷⁴Ge layer is doped with ⁷⁵As.

Thus, the desired Ge-based electron device which controls quantum chaosis obtained.

According to the sixth embodiment, the following advantages are achievedin addition to the advantages achieved by the fifth embodiment. That is,since the NTD is employed for forming the localization layer 44 which isformed from Ge doped with As, no crystal defect is generated during thedoping in principle and the crystallinity of the localization layer 44is not damaged unlike the case with a doping by the thermal diffusion orthe ion implantation, thereby making it possible to obtain an electrondevice which controls quantum chaos of excellent properties.

Though the specific descriptions of the embodiments of the invention aregiven in the foregoing, the invention is not limitedby the foregoingembodiments, and various modification are easily accomplished based onthe technical scope of the invention.

For instance, the values, structures, shapes, and materials used in theforegoing embodiments are given only by way of example, and it ispossible to use different values, structures, shapes, and materials ifnecessary.

Further, it is needless to say that the NTD method employed in the sixthembodiment is applicable not only to the double heterojunction formationbut also to a single heterojunction formation.

Also, it is possible to perform a modulation doping by applying the NTDmethod to the tunnel barriers 43 and 45 in the sixth embodiment. Morespecifically, the modulation doping of the n-type impurity is performedby forming undoped Si_(z) ⁷⁴Ge_(1-z) layers as the tunnel barriers 43and 45 in place of the undoped Si_(z) ⁷²Ge_(1-z) layers and thenirradiating the undoped Si_(z) ⁷⁴Ge_(1-z) layers with the monochromaticneutron beam to convert ⁷⁴Ge which is a part of the layers into ⁷⁵As.

1. An electron device which controls quantum chaos comprising: aheterojunction which is provided with a first region having an electronsystem characterized by quantum chaos and a second region having anelectron system characterized by integrability, the first region and thesecond region being adjacent to each other, and the heterojunction beingcapable of exchanging electrons between the first region and the secondregion, wherein a quantum chaos property of an electron system in asystem formed of the first region and the second region is controlled byapplying to the heterojunction an electric field having a componentperpendicular to at least a junction surface.
 2. The electron devicewhich controls quantum chaos according to claim 1, further comprising anelectrode for applying the electric field to the heterojunction.
 3. Theelectron device which controls quantum chaos according to claim 1,wherein the first region is in a metallic state, and the second regionhas a random medium.
 4. (canceled)
 5. (canceled)
 6. The electron devicewhich controls quantum chaos according to claim 1, wherein a maximumlength of the heterojunction in a direction along the junction surfaceis equal to or less than a coherence length of electrons.
 7. Theelectron device which controls quantum chaos according to claim 1,wherein each of the first region and the second region has the shape ofa layer.
 8. The electron device which controls quantum chaos accordingto claim 7, wherein the electrode for applying electric field to theheterojunction is formed, via an insulating film, on at least one of thefirst region and the second region each having the layer shape.
 9. Theelectron device which controls quantum chaos according to claim 1,wherein the quantum chaos property of the electron system of the systemformed of the first region and the second region is controlled bysetting a Fermi level of the electron system to a predetermined value inaddition to the application of electric field.
 10. The electron devicewhich controls quantum chaos according to claim 9, wherein the Fermilevel is set to the predetermined value by controlling a density of theelectron system.
 11. The electron device which controls quantum chaosaccording to claim 9, wherein critical electric field intensity withwhich a transition from quantum chaos to an integrable system occurs iscontrolled by the control on the Fermi level.
 12. The electron devicewhich controls quantum chaos according to claim 1, wherein a transferbetween the first region and the second region is equal to or less thana transfer of the first region and a transfer of the second region. 13.The electron device which controls quantum chaos according to claim 12,further comprising a tunnel barrier region formed between the firstregion and the second region.
 14. The electron device which controlsquantum chaos according to claim 13, wherein each of the first regionand the second region is formed from a semiconductor and the tunnelbarrier region is formed from a semiconductor of which energy at abottom of a conductive band is higher than that of the semiconductorused for forming the first region and the second region.
 15. Theelectron device which controls quantum chaos according to claim 13,wherein each of the first region and the second region is formed fromGaAs or InGaAs and the tunnel barrier region is formed from AlGaAs. 16.The electron device which controls quantum chaos according to claim 1,comprising a double heterojunction which is provided with the secondregion and the first regions disposed on each sides of the secondregion.
 17. The electron device which controls quantum chaos accordingto claim 16, wherein tunnel barrier regions are provided between thefirst region and the second region.
 18. The electron device whichcontrols quantum chaos according to claim 17, wherein each of the firstregions and the second region is formed from a semiconductor and each ofthe tunnel barrier regions is formed from a semiconductor of whichenergy at a bottom of a conductive band is higher than that of thesemiconductor used for forming the first regions and the second region.19. The electron device which controls quantum chaos according to claim17, wherein each of the first regions and the second region is formedfrom GaAs or InGaAs and the tunnel barrier regions are formed fromAlGaAs.
 20. A quantum chaos control method comprising: using aheterojunction which is provided with a first region having an electronsystem characterized by quantum chaos and a second region having anelectron system characterized by integrability, the first region and thesecond region being adjacent to each other, and the heterojunction beingcapable of exchanging electrons between the first region and the secondregion, and controlling a quantum chaos property of an electron systemin a system formed of the first region and the second region by applyingto the heterojunction an electric field having a component perpendicularto at least a junction surface.
 21. The quantum chaos control methodaccording to claim 20, wherein the quantum chaos property of theelectron system of the system formed of the first region and the secondregion is controlled by setting a Fermi level of the electron system toa predetermined value in addition to the application of electric field.22. The quantum chaos control method according to claim 20, wherein atransfer between the first region and the second region is equal to orless than a transfer of the first region and a transfer of the secondregion.